With respect to an investment-banking relationship in the recommendation game, the data support Keon’s cautionary comments. Interestingly, although investors appear to recognize this feature, they underreact to it.
Part VI Options, Futures, and Foreign Exchange
Chapter 19 Options: How They’re Used, How They’re Priced, and How They Reflect Sentiment
And now for something completely different: In developing the behavioral implications for options, I will not dwell on “hockey stick” charts, binomial trees, or the derivation of the Black-Scholes formula. At most I will remind readers about a few basics, and concentrate on behavioral issues concerning how options are used, priced, and reflect sentiment.
This chapter discusses the following:
• the role played by frame dependence in explaining the popularity of covered-call writing
• the role of reference points in determining how employees decide when to exercise company stock options
• how heuristic-driven bias moves so-called “implied volatility” away from actual volatility
• two related phenomena, “crashophobia,” and the “crash premium,” that stem from the effect of the 1987 stock market crash
• how investor sentiment affects and is reflected by option trading
Covered-Call Writing by Individual Investors
An investor who sells a call option on a stock in his portfolio is said to write a covered call. I have a colleague who has been trading options for about thirty years.1 Most of his option-trading activity involves covered-call writing on stocks in his retirement accounts.2 He does a good job describing how he uses options. Below I provide his comments using a question-and-answer format.
Q: When did you start trading options, and what strategy did you pursue?
A: Thirty years ago, I would consider a stock. My broker would tell me it looked good, that the analyst rated it as a strong buy. But I wasn’t always as sanguine as the analyst. The broker suggested that maybe the options route would be better.
So, I would buy call options on the stock. But my results were mixed using this approach. I won some, lost some, and broke about even.
Q: It sounds like most of the call options that you bought expired worthless. What happened next?
A: So I’m saying, Who’s on the other side? Someone is on the other side. Maybe that’s the side I should be on. But I didn’t want to sell uncovered calls. So, I asked myself, How do you play it the other way? I found a broker who was doing covered call writing. Now I’ve been doing it a good twenty-five years.
Q: Can you describe what typically happens when you engage in covered-call writing?
A: Here is a classical success story for me. In February 1998, I bought Cooper Cameron stock at $55.19 a share, including commission. At the same time, I sold a May 60 call for $3.875. The option expired on May 16, when the stock was trading at 62. So I made $3.88 plus $4.75 on a $55 stock in three months, more than if I had just bought the stock.
Q: Do they all work out that way?
A: Here’s one that didn’t work out so well. Boston Chicken:3 I bought the stock at $12 in October ’97. The broker was really hot on it, and the report from Prudential was really good. The price was way down, but I kept hearing that the stock was going to come back. At the same time, I sold the November call at 1.5. Then in November, I sold the January call at 15/16. That was a good premium, so I felt I was covered down to 10. It’s now at 3. I still have it. Before continuing with the interview, I want to put some of my colleague’s remarks into perspective. Meir Statman and I (Shefrin and Statman 1993a), report that covered-call writing is the most popular option-trading technique that individual investors use. Most investors eventually discover what my colleague realized early on: the majority of call options expire worthless.
A lot of the marketing literature on options that targets individual investors emphasizes covered-call writing. The Personal Money Guide published by the Research Institute of America (RIA) suggests that investors think of the premiums they receive from writing calls as “premium dividends.” Apparently, brokers too have figured this out. Here is an approach suggested by Leroy Gross (1982) in his manual for stockbrokers.
Joe Salesman: You have told me that you have not been too pleased with the results of your stock market investments.
John Prospect: That’s right. I am dissatisfied with the return, or lack of it, on my stock portfolio. Joe Salesman: Starting tomorrow, how would you like to have three sources of profit every time you buy a common stock?
John Prospect: Three profit sources? What are they?
Joe Salesman: First, you could collect a lot of dollars—maybe hundreds, sometimes thousands—for simply agreeing to sell your just-bought stock at a higher price than you paid. This agreement money is paid to you right away, on the very next business day—money that’s yours to keep forever. Your second source of profit could be the cash dividends due you as the owner of the stock. The third source of profit would be in the increase in price of the shares from what you paid, to the agreed selling price.
By agreeing to sell at a higher price than you bought, all you are giving up is the unknown, unknowable profit possibility above the agreed price. In return, for relinquishing some of the profit potential you collect a handsome amount of cash that you can immediately spend or reinvest, as you choose. (p. 166)
Individual investors find the lure of three sources of profit appealing. This is a clear case of frame dependence, and it illustrates the concepts I described in chapter 3. Psychologically speaking, many investors savor the three sources of profit separately rather than appreciating the integrated total return. You can see segregation at work in my colleague’s Cooper Cameron example, when he reported the two gains from his trading strategy separately. And what about dividends? In behavioral finance, dividends and covered-call writing go hand-in-hand. Here is my colleague’s view on that subject.
Q: Can you explain how you feel about dividends, and why?
A: I love dividends. They are a very pleasant part of investing. It’s real, in my pocket. My family history was tied up with bonds, not stocks. Receiving dividends is like receiving bond coupons.
In prior days, dividends gave a reasonable return. But not today and not on NASDAQ stocks, where I’ve had to create them for myself. I always like to have some stock in utilities. Like Puget Sound Power and Light. It’s given me a 9 percent return. It doubles every seven years, and I’ve had it for twenty years. Why did I buy it? It was in an area that was growing, in a good regulatory environment, and it paid dividends.
Covered-call writing is very appealing to investors who establish target prices for their stocks and plan to sell when the stock price reaches the target. In this respect, the calls they use are far out of the money, with the exercise price corresponding to their objective for the stock. Therefore, covered-call writers tend to let the stock get called away in situations where the market price lies above the exercise price on the expiration date. Of course, they could buy back the call, at a loss, if they wanted to keep those stocks. But if my colleague’s behavior is any indication, most do not buy back the option. My colleague says he usually lets the stock go.
The downside to covered-call writing is that the investor can lose out on a big gain if the underlying stock soars. Take Intel, whose stock price went up by a factor of two and a half between December 1995 and June 1998. My colleague tells me he has had Intel called away six times during this period.
Covered-Call Writing by Professional Investors
There are psychological reasons why individual investors find covered-call writing attractive. But the same may not be true for mutual fund managers. It may not be true if their investors focus not on segregated gains but on integrated returns. An article that appeared in the Wall Street Journal describes how covered-call writing adversely impacted the performance of Putnam’s Strategic Investments Trust.
Why this poor record? From its launch until 1991, the Putnam fun
d was a so-called option income fund, which meant it wrote call options against its stock portfolio in an effort to boost the income it paid to shareholders. The trouble was, by writing the options, the fund gave up the chance to earn healthy capital gains. The good stocks got called away by call-option buyers, who had purchased the right to buy the stocks. Meanwhile, the rotten stocks were left.4
Employee Stock Options
Employee stock options are especially interesting in that they lead employees to face a classic decision problem studied by psychologists Daniel Kahneman and Amos Tversky (1979). Either (1) exercise the option and take a certain gain, or (2) wait and take the chance that the company stock price will go even higher.
Chip Heath, Steven Huddart, and Mark Lang (1998) have analyzed the way that employees deal with this decision. Note that such employees have high-ranking positions, and so their stakes are considerable. Heath, Huddart, and Lang find that employees tend to exercise options when the stock price moves to a new maximum, relative to some maximum stock price achieved over the preceding eight months.
This behavior conceivably reflects at least three behavioral phenomena. First, employees might believe that little room for improvement remains on the upside, but considerable room remains on the downside, as per Werner De Bondt’s (1993) article about betting on trends. Second, employees may recall not having exercised an option at the previous high, and decide to do so now in order to avoid additional regret. Third, employees may be behaving in accordance with prospect theory (Kahneman and Tversky 1979). Heath, Huddart, and Lang suggest that employees set reference points at the eight-month maximum price. According to prospect theory, an employee would exhibit risk-seeking behavior, meaning she would hold the options when the current price was below her reference point, and display risk averse behavior (exercise) when the current price moved above her reference point.
A Practical Perspective on Option Pricing Theory
Academics have developed elaborate and elegant theories about the factors that determine option prices. The best known of these is the option pricing model developed by Fischer Black and Myron Scholes (1973). Readers will gain little by my specifying the Black-Scholes formula. But I do need to indicate something about the arguments that appear in the formula. The formula stipulates that the price of an option depends on five arguments: the concurrent price of the underlying asset, the return volatility on the underlying asset, the exercise price on the option, the time to expiration, and the risk-free interest rate. Notably, the Black-Scholes formula is based on assumptions such as lognormality, constant volatility, and an invariant risk-free rate over the life of the option, a point to which I return below.
The Black-Scholes formula provides an elegant options-pricing theory. That being said, option trader and author Sheldon Natenberg (1988, 1997) suggests that “a trader who becomes a slave to a theoretical pricing model is almost certain to have a short and unhappy trading career.”5
Option traders face innumerable risks. Natenberg divides these risks into three categories. The first category is input risk—risk to be faced when option prices behave in accordance with Black-Scholes. These risks are associated with the option Greeks—delta, gamma, theta, vega, and rho.6
The second risk category is assumption risk—risk that the theoretical models used to value options are inappropriate. Natenberg mentions several reasons why this might be the case. For example, the underlying price distribution may not be lognormal; or the volatility over the life of the contract may not be constant.
Then there are practical risks. Here are two examples. (1) A trader may not have sufficient capital to meet subsequent margin requirements. (2) A short option position may be at-the-money on the expiration date, leading the trader to be uncertain whether or not he will have to supply the underlying security.
Of the different types of risk, the one most relevant to behavioral finance is assumption risk. The Black-Scholes model is indeed very elegant. But when you get right down to it, isn’t it just another heuristic, capable of producing heuristic-driven bias? Let’s see.
Implied Volatility
Of the five arguments used in the Black-Scholes formula, four are observable and one is not. The unobservable argument is volatility, the standard deviation of the distribution governing the future return on the underlying security. However, one variable that can be observed is the option price, the output from a Black-Scholes formula. This has given rise to the practice of inverting the Black-Scholes formula and using the current option price, together with the four input variables, to infer the market’s belief about future volatility. This volatility is known as the implied volatility of the option.
Let’s consider an example using index options, which are options traded on the S&P 500. On May 19, 1998, the S&P 500 closed at 1108.73. On that day a variety of options were traded on the index. These varied by month of expiration and exercise (strike) price. The expiration months available for trade were June, July, August, September, and December of 1998, and March, June, and December of 1999.
The available exercise prices for each expiration month spanned a wide range. For the June’98 options, the lowest available exercise price was 625, and the highest was 1350. One thing that all the June’98 options shared in common was that they were based on the same underlying asset—the S&P 500. The distribution of future returns on this asset has but one volatility. Therefore, in theory, the implied volatility of all the S&P 500 index options should be the same, regardless of exercise price, and regardless of whether the option is a call or a put.
Figure 19-1 displays two curves of implied volatility relative to exercise price on May 19, 1998, one for June’98 call options, and the other for June’98 put options. In theory, the figure should display a single horizontal line, with one curve lying on top of the other. Is that what we see?
Two features in figure 19-1 are striking. First, the implied volatility curves for call options and put options do not lie on top of each other: The curve for calls is higher. Second, the implied volatility curve is downward sloping. Volatility is high for low exercise prices, declining as the exercise price gets closer to the current price. These curves are very different from a horizontal line, which is the theoretical pattern. Because of its shape, the actual pattern has come to be called a smile (a crooked smile perhaps, but a smile nonetheless). The actual smile pattern, in contrast to the theoretical flat pattern, suggests that assumption risk is real.
Now take a close look at the magnitudes of the implied volatilities displayed in figure 19-1. Notice that they range from about 100 percent at the left end of the spectrum to less than 20 percent at the right end. What are we to make of such huge discrepancies between numbers that are supposed to be the same, at least in theory?
Figure 19-1 Implied Volatilities for the S&P 500, May 19, 1998
The chart of Black-Scholes implied volatilities, on May 19, 1998, for the S&P 500, across exercise prices. On that day the S&P 500 closed at 1108.73. In theory, there is only one implied volatility that is the same for puts and calls, and all exercise prices. In practice, the pattern has come to be called a smile when it turns up on both the right and left. In this figure, the pattern is closer to a sneer. The steepness of these curves on the left suggests that investors are disproportionately concerned about a sharp drop in the market—in other words, that they suffer from “crashophobia.”
The Impact of the Crash of 1987 on Implied Volatilities
Jens Jackwerth and Mark Rubinstein (1996) point out that historical volatility has been about 20 percent. But volatility is itself volatile. If we were to look at volatility every April during the period 1986–1993, we would see that it fluctuated between 11.8 percent and 23.8 percent when measured over a three-year window. For a twelve-month window, the range was higher, with a low of 10 percent, and a high of 34.8 percent. Note that the 34.8 percent figure, which is exceptionally high, includes October 1997, when the U.S. stock market crashed. The next highest figure is 17 percent. The figure
s for narrower windows (twenty-eight days and ninety-one days) are similar to those for the twelve-month window.
Figure 19-2 shows how volatility has varied in the period October 1995 through May 1998. The data in this figure should be interpreted as volatility in the S&P 500 index, measured over moving windows that are forty days wide. Notice that actual volatility fluctuated between 8
Figure 19-2 Volatility, S&P 500
How volatile is the return on the S&P 500? Return standard deviation ranged from below 10 percent to above 25 percent between November 1995 and June 1998. percent and 28 percent during this time, and was actually below 15 percent much of the time. This range is similar to the ranges reported by Jackwerth and Rubinstein.
Take another look at figure 19-1. The implied volatilities for the lowest call exercise prices are near 100 percent.7 On October 19, 1987, the day of the crash, the two-month S&P futures price declined 29 percent. As was mentioned above, the volatility from April 1987 through April 1988 was 34 percent, far less than 100 percent or even the corresponding 60 percent figure for puts. What is going on?
As Jackwerth and Rubinstein document, the 1987 crash changed a lot of things. Before the crash, implied volatilities were much the same for different exercise prices. After the crash, the smile patterns emerged. What do those smile effects tell us?
One thing they tell us is that option traders do not accept the lognormal assumption in the Black-Scholes framework. Given the range of implied volatilities that existed before 1987, lognormality implies that the magnitude of the decline on October 19, 1987, is almost impossible. In fact, the lognormal assumption with historically observed volatility levels implies that over a twenty-billion-year time span—the life of the universe—the expected number of stock market crashes like the one experienced in 1987 is less than one!
Beyond Greed and Fear Page 34